On the relevance of weak measurements in dissipative quantum systems

TL;DR

This paper examines how dissipation affects weak measurements in quantum systems, revealing that dissipation causes weak values to converge to expectation values in non-degenerate systems, while they can remain anomalous in degenerate systems, and proposes methods to extract dissipative dynamics information.

Contribution

It provides new insights into the behavior of weak values under dissipation and introduces techniques to probe dissipative dynamics using weak measurements.

Findings

Weak values converge to expectation values in non-degenerate systems with dissipation.

Weak values can remain anomalous in degenerate systems despite dissipation.

Weak measurements can differentiate between Markovian and non-Markovian dissipative dynamics.

Abstract

We investigate the impact of dissipation on weak measurements. While weak measurements have been successful in signal amplification, dissipation can compromise their usefulness. More precisely, we show that in systems with non-degenerate eigenstates, weak values always converge to the expectation value of the measured observable as dissipation time tends to infinity, in contrast to systems with degenerate eigenstates, where the weak values can remain anomalous, i.e., outside the range of eigenvalues of the observable, even in the limit of an infinite dissipation time. In addition, we propose a method for extracting information about the dissipative dynamics of a system using weak values at short dissipation times. Specifically, we explore the amplification of the dissipation rate in a two-level system and the use of weak values to differentiate between Markovian and non-Markovian dissipative dynamics. We also find that weak measurements operating around a weak atom-cavity coupling can probe the atom dissipation through the weak value of non-Hermitian operators within the rotating-wave approximation of the weak interaction.